Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nurbs-1.3.6 / basisfun.m

diff --git a/octave_packages/nurbs-1.3.6/basisfun.m b/octave_packages/nurbs-1.3.6/basisfun.m
new file mode 100644 (file)
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+++ b/octave_packages/nurbs-1.3.6/basisfun.m
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+function B = basisfun (iv, uv, p, U)
+
+% BASISFUN:  Basis function for B-Spline
+%
+% Calling Sequence:
+% 
+%   N = basisfun(iv,uv,p,U)
+%   
+%    INPUT:
+%   
+%      iv - knot span  ( from FindSpan() )
+%      uv - parametric points
+%      p  - spline degree
+%      U  - knot sequence
+%   
+%    OUTPUT:
+%   
+%      N - Basis functions vector(numel(uv)*(p+1))
+%   
+%    Adapted from Algorithm A2.2 from 'The NURBS BOOK' pg70.
+%
+% Copyright (C) 2000 Mark Spink
+% Copyright (C) 2007 Daniel Claxton
+% Copyright (C) 2009 Carlo de Falco
+%
+%    This program is free software: you can redistribute it and/or modify
+%    it under the terms of the GNU General Public License as published by
+%    the Free Software Foundation, either version 2 of the License, or
+%    (at your option) any later version.
+
+%    This program is distributed in the hope that it will be useful,
+%    but WITHOUT ANY WARRANTY; without even the implied warranty of
+%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%    GNU General Public License for more details.
+%
+%    You should have received a copy of the GNU General Public License
+%    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+B = zeros(numel(uv), p+1);
+                                               
+for jj = 1:numel(uv) 
+
+  i = iv(jj) + 1; %% findspan uses 0-based numbering
+  u = uv(jj);
+
+  left = zeros(p+1,1);
+  right = zeros(p+1,1);
+
+  N(1) = 1;
+  for j=1:p
+    left(j+1) = u - U(i+1-j);
+    right(j+1) = U(i+j) - u;
+    saved = 0;
+
+    for r=0:j-1
+      temp = N(r+1)/(right(r+2) + left(j-r+1));
+      N(r+1) = saved + right(r+2)*temp;
+      saved = left(j-r+1)*temp;
+    end
+    
+    N(j+1) = saved;
+  end
+
+  B (jj, :) = N;
+
+end
+
+end
+
+%!test
+%!  n = 3; 
+%!  U = [0 0 0 1/2 1 1 1]; 
+%!  p = 2; 
+%!  u = linspace (0, 1, 10);  
+%!  s = findspan (n, p, u, U);  
+%!  Bref = [1.00000   0.00000   0.00000
+%!          0.60494   0.37037   0.02469
+%!          0.30864   0.59259   0.09877
+%!          0.11111   0.66667   0.22222
+%!          0.01235   0.59259   0.39506
+%!          0.39506   0.59259   0.01235
+%!          0.22222   0.66667   0.11111
+%!          0.09877   0.59259   0.30864
+%!          0.02469   0.37037   0.60494
+%!          0.00000   0.00000   1.00000];
+%!  B = basisfun (s, u, p, U);
+%!  assert (B, Bref, 1e-5);